Dear All,
I would like to inform you of a new exiting project that it
taking place at Harvard this academic year -- the "Exploring the
Frontiers of Incompleteness" project, made possible by the
generous support of the John Templeton Foundation. The aim is to
bring together some of the most prominent thinkers who have
struggled with the following questions:
1. Do the questions that are independent of the standard
axioms admit of determinate answers?
2. If so then what are those answers and how might we go
about determining them?
These are very difficult questions and there are many prominent
philosophers and mathematicians who have given them a great deal
of thought. There is a broad spectrum of views. For example, at
one end there are people like Solomon Feferman who think that
there are "objective facts of the matter" about questions
pertaining to the natural numbers but think that most of the
questions of set theory (most notably, the Continuum
Hypothesis (CH)) are "indeterminate" since the underlying notions
of set theory are "inherently vague". At the other end of the
spectrum there are people like Hugh Woodin who have provided
serious arguments (based on a wealth of mathematical results) for
thinking that questions like CH are determinate and who have
advanced major programs (again based on a wealth of mathematical
results) for determining those answers. There are many views in
between and there are views which are entirely orthogonal to this
ordering. The main purpose of the two-part series is to
investigate these various positions, compare their strengths and
weaknesses, and make steps forward in determining the answers to
the two guiding questions. We shall do this by actually engaging
with the major figures in this foundational debate. Through
generous external support we have managed to secure the funding
necessary to make this possible. Over the next two semesters
there will be 12 workshops. Each workshop will involve a
presentation by one of the major figures in the debate. The
speakers are:
Fall Semester
* Solomon Feferman
* Matt Foreman
* Penelope Maddy
* Charles Parsons
* William Tait
* Hugh Woodin
Spring Semester
* James Cummings
* Tony Martin
* Menachem Magidor
* John Steel
* Stevo Todorcevic
* Philip Welch
The speaker presentations will occur (roughly) every two weeks
and during the intervening weeks there will be lectures by Peter
Koellner on the background material required for the upcoming
talk. In addition, the paper of the presentation will be made
available in advance. Moreover, all 12 speakers will be involved
throughout the process - they too will receive the papers in
advance and will be given an opportunity to comment on it. At
the end of the workshop series there will be a
master-workshop (something like a conference but more
interactive) involving all workshop-speakers and all
participants. Finally, along the way there will be opportunity
for world-wide discussion on an Internet portal.
For further details are available here: Go to
http://logic.harvard.edu/#
and then click on ``EFI Project'' to navigate through the
Overview, Schedule, and Materials and Discussion section.
We hope that you can all participate.
Best,
Peter Koellner